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Thursday, July 03, 2008

Riemann Hypothesis

OK, I suppose I must provide a link to the new paper by Xian-Jin Li with the simple title A proof of the Riemann hypothesis. Like many around the blogosphere, I have no intention of trying to decipher it, although the claimed proof, by a well known number theorist, relies heavily on Fourier analysis and ideas from Connes NCG. In other words, it sounds highly promising. Despite the expertise of the author however, my hunch is that there's a flaw, because the claimed proof is mostly standard analysis. However, perhaps flaws in the proof will be easy to iron out using techniques from quantum information theory.

Update:Terence Tao believes there is an error in equation (6.9) on page 20. He comments that the Fourier transform really ought not to be this powerful. Given the standard analytical form of Fourier transform used in the claimed proof this would seem a reasonable statement, but perhaps in an $\omega$ categorical framework (where as usual we associate primes $p$ with categorical dimension) this could be modified to obtain a decomposition of the form (6.9).

6 Comments:

The proof is now up to version 3. In that version, there is a change to the definition of equation (6.9). I wonder if Terry was looking at the latest version.

But you don't have time to explore this as you are busy working on that damned mixing matrix. Meanwhile, I'm most of the way done with a post on the circulants and electroweak unification but am too tired to complete it tonight.

Hmm.. I find it hard to believe that this guy would make an error as basic as that. He is no crank; MathSciNet tells us at he has had several publications in some of the best journals (Proc. Amer. Math. Soc. , IMRN,... ) over the last few years..

"If you have not made a mistake, you have not been a GREAT scientist!""Even David Hilbert was wrong!"-- Dr. Wolfgang Haken, private communication[ he proved 4-color Theorem with K. Appel, using computer proof. His father was Max Planck's PhD student. We were talking about cosmology, he was dabbling in it in his retirement years ]

So, basically what I'm saying is that the big achievers (fueled by big ego) take big risks. "It goes with the terriroty", that failure comes with success.

"In order to win, you have learn how to lose"-- sports saying

"In order to push the limits, you sometimes have to EXCEED the limits"-- B. Varsha, Australian F1 Grand Prix

There was an interesting story about Linus Pauling (the famous Caltech Nobel Laureate, who had a "godlike reputation: anything he wanted to do..he could do it"). They were talking about his track record, & R. Feynman brought up the fact that he was wrong quite a few times.

Q: "How do you get good ideas?"L. Pauling: "I try a LOT of ideas"

I.e., the "shotgun effect" works in Research, as well as target shooting.

Similar anecdote for a successful businessman:

Q: How did you become wealthy?A: By making a lot of mistakes!Q: What!?A: I learned from my mistakes

So, while people ridicule XXX for a mistake, XXX keeps on trying. Probably succeed in the end.

"Victory belongs to the most PERSEVERING"-- Napoleon

Kea certainly has that persevering mentality, so..victory is an eventuality ("it's not a matter of IF, but WHEN")

RIsk Management

quote by Bobby Baldwin, champion poker player & successful Las Vegas casino executive (friend of mine). He lost money, won a ton, lost it, won the Poker championship (youngest winner at the time), then quit ("quit while you're ahead") to become a casino executive (more stable occupation). Smart.

Classic contrast in "risk management": Bernard Montgomery VS George Patton. 2 Allied generals in WWII, but very opposing philosophies. BM was extremely conservative (to his detriment), while GP was extremely agressive (to his detriment). There is a balance between aggression & conservative.

"It is better to err on the aggressive side, than being conservative"

It is a well known phenomena in Sports (similar to Science Research, it's a battle between competitive groups), that a team that goes into a "defensive shell" (conservative, protecting a lead) begins to lose its offense (aggression).